The noise in the circular law and the Gaussian free field

Fill an n x n matrix with independent complex Gaussians of variance 1/n. As n approaches infinity, the eigenvalues {z_k} converge to a sum of an H^1-noise on the unit disk and an independent H^{1/2}-noise on the unit circle. More precisely, for C^1 functions of suitable growth, the distribution of sum_{k=1}^n (f(z_k)-E f(z_k)) converges to that of a mean-zero Gaussian with variance given by the sum of the squares of the disk H^1 and the circle H^{1/2} norms of f. Moreover, with p_n the characteristic polynomial, log|p_n|- E log|p_n| tends to the planar Gaussian free field conditioned to be harmonic outside the unit disk. Finally, for polynomial test functions f, we prove that the limiting covariance structure is universal for a class of models including Haar distributed unitary matrices.Comment: 30 pages, 5 figures. Revised introduction. New section

Cooperating to Resist Coercion: An Experimental Study

This study sheds light on the difficulties people face in cooperating to resist coercion. We adapt a threshold public goods game to investigate whether people are able to cooperate to resist coercion despite individual incentives to free-ride. Behavior in this resistance game is similar to that observed in multi-period public goods games. Specifically, we observe "out-of-equilibrium" outcomes and a decrease in successful resistance in later periods of a session compared to earlier ones. Nevertheless, cooperation remains relatively high even in the later periods. Finally, we find that increasing the resistance threshold has a substantial negative effect on the probability of successful resistance.

Alcohol and Analgesic Use in the Baby Boomer Cohort

If the population bubble known as the Baby Boomers continue to consume alcohol at higher than expected levels as they age into the middle and older adult categories it could have a substantial impact on future health care needs. This problem will be compounded if Boomers also take analgesic (pain-relief) medications when consuming alcohol. The objective of this study is to determine the prevalence of alcohol and analgesic usage in the Baby Boomer cohort and to ascertain whether there is an association between alcohol, analgesics, and pain. Drinking alcohol while also taking analgesics can have serious health consequences and, depending on the type of analgesic, could result in acute liver failure or other serious health problems. Data were analyzed from the 1999-2000 National Health and Nutrition Examination Survey (NHANES) for participants born during the Baby Boomer cohort years of 1946-1964. Analysis by SUDAAN indicated that approximately 67% of the Boomers are drinking alcohol beyond what is considered a moderate level by the CDC and NIAAA. More than half the respondents had used analgesics daily or almost every day for at least a month (females = 58.7%; males = 40.5%) and Boomers who are currently using analgesics (females = 19.35%; males = 16.34%). There was a significant association for respondents who reported consuming 12 or more drinks during the past 12 months and who were currently taking analgesics (p = 0.02). A statistically significant association found for respondents who reported experiencing persistent pain in the past 12 months and who had binged (5 or more drinks) at least once during the past 12 months with taking RX analgesics (CMH: p = 0.03, df = 1)

The roles of organic and inorganic zinc and selenium sources in the nutrition and promotion of health in rainbow trout (Oncorhynchus mykiss)

Merged with duplicate record 10026.1/761 on 13.03.2017 by CS (TIS)Three nutritional feeding trials were undertaken to investigate the nutritional role of zinc (Zn) and selenium (Se) in the promotion of health in rainbow trout (Oncorhynchus mykiss Walbaum). Organic and inorganic sources of both elements were assessed by determining bioavailability, effects on growth, feed utilisation, immuno-competence, oxidative status, fillet quality and interactions with other trace elements. A focus was made on the use of practical diets throughout the study. The first experiment assessed the bioavailability of residual Se and Zn from a white fishmeal based practical diet during a 10-week trial in comparison to diets containing either supplemental Se-yeast and Zn proteinate (Zn-pr) or sodium selenite (Na2SeOJ) and Zn sulphate (ZnS04). Se-yeast and Zn-pr were hypothesised to be more digestible and more effective in raising Se and Zn status than inorganic sources. Apparent digestibility of residual Zn and Se was 21.9% and 54.2% respectively. No conclusive difference in overall Zn bioavailability was observed between treatments. Se-yeast significantly increased Se digestibility to 63.7%, Se levels in all tissues, and the activities of hepatic thioredoxin reductase (Trx-R) and glutathione peroxidase (GSH-Px). Selenite supplementation only resulted in increased GSH-Px activity. Se-yeast was found to be a highly bioavailable Se source, effectively raising Se status. The second experiment determined the efficacy and effect on health of residual Zn in comparison to 125, 312 and 781 mg kgˉ¹ supplemented Zn-pr or Zn sulphate in a practical diet. It was hypothesised that Zn-pr would be more efficacious in the promotion of health than Zn sulphate. The retention of both Zn sulphate and Zn-pr followed the same exponential decay (R2 = 0.978) with increasing dietary Zn loading. This was accompanied with a lack of effect of 12-weeks Zn supplementation on standard growth rate (SGR), feed conversion ratio (FCR), Zn enzyme activity (Cu/Zn-superoxide dismutase and alkaline phosphatase), oxidative status (hepatic and pyloric caeca malondialdehyde (MDA), total plasma antioxidant capacity (TAC) and oxidative DNA damage), immuno-competence (superoxide generation, lysozyme and leukocyte counts), hematocrit, nuclear abnormalities (micronuclei, and notched and blebbed nuclei), and fillet quality (drip loss and astaxanthin). Both dietary Zn-pr (R2 = 0.573) and Zn sulphate (R2 = 0.453) interacted with hepatic manganese (Mn) but not with iron (Fe) or copper (Cu). No significant differences were observed between sources and a strict homeostatic regulation of dietary Zn in rainbow trout was observed. Preliminary investigations were carried out to establish the effects of seven days chronic husbandry related stressors on immuno-competence and oxidative status. It was hypothesised that chronic husbandry related stressors would result in oxidative stress and impaired immuno-competence. Alternating between netting and confinement stressors resulted in oxidative stress as determined by decreased TAC, increased oxidative DNA damage and modulated superoxide generation by leukocytes in the whole blood. The final experiments investigated the efficacy and effects on health of residual Se in comparison to 2, 4, and 8 mg kgˉ¹ supplemental sodium selenite or Se-yeast in a commercial trout grower diet. It was hypothesised that supplemental Se would confer benefits to the health of both stressed and un-stressed fish, and Se-yeast would be more efficacious than selenite in its effects. Following a 10-week trial, the implication of seven days husbandry related stressors were also evaluated. Se retention was reduced in fish fed selenite up to 4 mg kgˉ¹ in comparison to fish fed the basal diet; in contrast Se-yeast increased Se retention. SGR, FCR, hepatic GSH-Px and Trx-R, plasma TAC, hepatic MDA, respiratory burst, lysozyme, nuclear abnormalities, and hematocrit were not affected by the supplemented dietary Se. However, in pre-stress fish fillet quality (drip loss) may be improved by Se-yeast supplementation; this was not observed with selenite. Stress decreased whole body Se in all treatments and increased GSH-Px to the greatest extent in Se supplemented diets suggestive of an increased Se utilisation during stress. Se had no protective effects on immuno-competence and oxidative status post stress. On the contrary, 8 mg kgˉ¹ Se from selenite increased hepatic MDA and resulted in the lowest GSH-Px increases amongst supplemented fish, which may be indicative of the sub-lethal effects of Se in fish fed a high level of inorganic Se; this was not observed with Se-yeast. Selenite (R² = 0.6611), but not Se-yeast (R² = 0.073), significantly interacted with whole body Cu. No interactions were found between dietary Se and Fe or Mn. Levels of whole body Fe, Mn, Cu and Zn were not affected by husbandry related stressors. The study concludes that Se-yeast supplemented in fishmeal based diets is more bioavailable and efficacious in the maintenance of health than selenite. The efficacy of Zn-pr was not distinguished from that of Zn sulphate in the supplementation of practical diets. No difference was observed between Zn-pr and Zn sulphate in terms of bioavailability or efficacy. This may be due to the tight homeostatic regulation of dietary Zn above marginal levels. Se utilisation may increase during chronic husbandry related stress. Due to the lack of any measurable toxic effects and increased retention, Se-yeast may be more suitable for the delivery of Se in fish exposed to husbandry related stress, which was shown to result in oxidative stress. Higher quality practical diets may meet requirements for Se in un-stressed fish, but in conditions of stress, maximal GSH-Px and Se status may only be achieved by diets containing supplemental Se

A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (p.d.f.) of the random shear tensor at a general point in the lens plane due to point masses in the limit of an infinite number of stars. Up to this order, the p.d.f. depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the stars' masses. As a consequence, the p.d.f.s of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the limit of an infinite number of stars is also presented. Extending to general random distributions of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of {\it global} expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars.Comment: To appear in JM

Harmonics added to a flickering light can upset the balance between ON and OFF pathways to produce illusory colors

The neural signals generated by the light-sensitive photoreceptors in the human eye are substantially processed and recoded in the retina before being transmitted to the brain via the optic nerve. A key aspect of this recoding is the splitting of the signals within the two major cone-driven visual pathways into distinct ON and OFF branches that transmit information about increases and decreases in the neural signal around its mean level. While this separation is clearly important physiologically, its effect on perception is unclear. We have developed a model of the ON and OFF pathways in early color processing. Using this model as a guide, we can produce imbalances in the ON and OFF pathways by changing the shapes of time-varying stimulus waveforms and thus make reliable and predictable alterations to the perceived average color of the stimulus—although the physical mean of the waveforms does not change. The key components in the model are the early half-wave rectifying synapses that split retinal photoreceptor outputs into the ON and OFF pathways and later sigmoidal nonlinearities in each pathway. The ability to systematically vary the waveforms to change a perceptual quality by changing the balance of signals between the ON and OFF visual pathways provides a powerful psychophysical tool for disentangling and investigating the neural workings of human vision

Central limit theorems for the real eigenvalues of large Gaussian random matrices

Let G be an N×N real matrix whose entries are independent identically distributed standard normal random variables Gij∼N(0,1). The eigenvalues of such matrices are known to form a two-component system consisting of purely real and complex conjugated points. The purpose of this paper is to show that by appropriately adapting the methods of [E. Kanzieper, M. Poplavskyi, C. Timm, R. Tribe and O. Zaboronski, Annals of Applied Probability 26(5) (2016) 2733–2753], we can prove a central limit theorem of the following form: if λ1,…,λNR are the real eigenvalues of G, then for any even polynomial function P(x) and even N=2n, we have the convergence in distribution to a normal random variable 1E(NR)−−−−−√⎛⎝∑j=1NRP(λj/2n−−√)−E∑j=1NRP(λj/2n−−√)⎞⎠→N(0,σ2(P)) as n→∞, where σ2(P)=2−2√2∫1−1P(x)2dx

Measurement and Compensation of Horizontal Crabbing at the Cornell Electron Storage Ring Test Accelerator

In storage rings, horizontal dispersion in the rf cavities introduces horizontal-longitudinal (xz) coupling, contributing to beam tilt in the xz plane. This coupling can be characterized by a "crabbing" dispersion term {\zeta}a that appears in the normal mode decomposition of the 1-turn transfer matrix. {\zeta}a is proportional to the rf cavity voltage and the horizontal dispersion in the cavity. We report experiments at the Cornell Electron Storage Ring Test Accelerator (CesrTA) where xz coupling was explored using three lattices with distinct crabbing properties. We characterize the xz coupling for each case by measuring the horizontal projection of the beam with a beam size monitor. The three lattice configurations correspond to a) 16 mrad xz tilt at the beam size monitor source point, b) compensation of the {\zeta}a introduced by one of two pairs of RF cavities with the second, and c) zero dispersion in RF cavities, eliminating {\zeta}a entirely. Additionally, intrabeam scattering (IBS) is evident in our measurements of beam size vs. rf voltage.Comment: 5 figures, 10 page

The BetaCage, an ultra-sensitive screener for surface contamination

Material screening for identifying low-energy electron emitters and alpha-decaying isotopes is now a prerequisite for rare-event searches (e.g., dark-matter direct detection and neutrinoless double-beta decay) for which surface radiocontamination has become an increasingly important background. The BetaCage, a gaseous neon time-projection chamber, is a proposed ultra-sensitive (and nondestructive) screener for alpha- and beta-emitting surface contaminants to which existing screening facilities are insufficiently sensitive. Sensitivity goals are 0.1 betas per keV-m$^2$-day and 0.1 alphas per m$^2$-day, with the former limited by Compton scattering of photons in the screening samples and (thanks to tracking) the latter expected to be signal-limited; radioassays and simulations indicate backgrounds from detector materials and radon daughters should be subdominant. We report on details of the background simulations and detector design that provide the discrimination, shielding, and radiopurity necessary to reach our sensitivity goals for a chamber with a 95$\times$95 cm$^2$ sample area positioned below a 40 cm drift region and monitored by crisscrossed anode and cathode planes consisting of 151 wires each.Comment: 5 pages, 3 figures, Proceedings of Low Radioactivity Techniques (LRT) 2013, Gran Sasso, Italy, April 10-12, 201

The Littlewood-Gowers problem

We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times (log p)^{1/2 - \epsilon} as p tends to infinity. This improves on the exponent 1/3 in recent work of Green and Konyagin.Comment: 31 pp. Corrected typos. Updated references